The Mamelodi Sundowns midfielder, who spent last season on loan at National First Division side Santos, joins compatriot Mark Mayambela at the club.
He has been signed to cover a number of positions across the park and will hope to extend his deal with an influential second half of the season.
“He is an interesting player who can play in many positions,” Djurgardens sports director Bosse Andersson told the club’s website.
“He has made a very good impression since he came here to on trial in early July.”
Andersson says it could be the start of more player moves from “South Africa’s biggest club”.
“We have begun a good cooperation with Mamelodi Sundowns who is South Africa's biggest club,” a comment likely to earn the ire of Kaizer Chiefs and Orlando Pirates fans.
The 22-year-old Mdaki has been given the number 17 jersey this season.